What is (x+i-ix^2)^2 ?

The solution to (x+i-ix^2)^2 is (-x^4+3x^2-1)+(2x-2x^3)i

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simplify (x+i-ix^2)^2

simplify

(x + i - i x^{2})^{2}

(- x^{4} + 3 x^{2} - 1) + (2 x - 2 x^{3}) i

Solution steps

(x + i - i x^{2})^{2}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(x + i - i x^{2})^{2} = (x + i - i x^{2}) (x + i - i x^{2})

= (x + i - i x^{2}) (x + i - i x^{2})

Distribute parentheses

= xx + x i + x (- i x^{2}) + i x + ii + i (- i x^{2}) - i x^{2} x - i x^{2} i - i x^{2} (- i x^{2})

Simplify

xx + x i + x (- i x^{2}) + i x + ii + i (- i x^{2}) - i x^{2} x - i x^{2} i - i x^{2} (- i x^{2}) : - x^{4} + 3 x^{2} + 2 x i - 2 x^{3} i - 1

= - x^{4} + 3 x^{2} + 2 x i - 2 x^{3} i - 1

Rewrite in standard complex form:

(- x^{4} + 3 x^{2} - 1) + (2 x - 2 x^{3}) i

= (- x^{4} + 3 x^{2} - 1) + (2 x - 2 x^{3}) i

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